Quiz

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A function is a mapping between an input and an output. For example, the function \(f(x) = x^2\) takes an input, \(x,\) and returns its square, \(x^2.\) In this case, \(f(2) = 2^2 = 4,\) \(f(\sqrt{3}) = \left(\sqrt{3}\right)^2 = 3,\) and so on. The key difference between a function and a more general relation is that for every input to a function, there is exactly one output.

Sometimes when mapping between an input and output the input can be another function, that maps to another input. This is called a composite function . When evaluating a composite function, first we compose the function and evaluate the result as we do any other function

Given that \(f(x)=\frac{3x}{x-1}\) and \(g(x)=\frac{x}{1-2x}\) what is the value of the function \((f \circ g)(x)\) at \(x=1\)?

Given the following function:

Based on the piecewised function above, if \(x>3,\) we evaluate over the function \(f(x)=3x+1.\) If \(x\) is between \(-1\) and \(3\) inclusive, then we evaluate over the function \(f(x)=2x.\) If \(x<-1,\) we evaluate over the function \(f(x)=3.\)